Figure 9: The calculated real and imaginary parts of the
dielectric function for LiBH4
In figure (9) blue line indicates the real part, while red line shows
imaginary part of dielectric function. The static value of the real part
of the dielectric function at zero frequency is found to be 2.25. It
extends slightly along the frequency axis upto 5 eV, however, beyond
this frequency, its value ascends at the higher frequency and gains
maximum value of 5.6. Nevertheless, on increasing the frequency above
7.5 eV, \(\varepsilon_{1}\) descends to zero at 9 eV, it further extends
towards its negative values and gains the value of -2 at 10.5 eV
frequency. On escalation of the frequency range above 10.5 eV, real part
of dielectric function regains its value. After crossing the frequency
axis at 14 eV, it extends with positive values but almost parallel to
the frequency axis. Moreover, as revealed from figure (9),\(\varepsilon_{2}\) the imaginary value of the dielectric function
remains zero upto an energy (frequency) approximately equal to the
energy band of the studied material. However, beyond ⁓ 6.88 eV
frequencies, the value of \(\varepsilon_{2}\) is noticed to be increased
sharply and attains maximum value (5.7) at 8.7 eV frequency.
Unfortunately, after that frequency the values of imaginary constant
started to decrease and becomes zero at 13 eV frequency.
Refractive index and extinction coefficient
A dimensionless parameter, the refractive index, is in fact a ratio amid
velocity of light in a vacuum to the velocity of light passing through
the materials. The refractive index, n and dielectric functions
(\(\varepsilon_{1}\), \(\varepsilon_{2}\)) are interlinked through the
following relations [40]:
\(\varepsilon_{1}=n^{2}-k^{2}\)(3)\(\backslash n\varepsilon_{2}=2nk\) (4)
Where \(k\) defines the extinction coefficient. Figure 10 displays the
material’s response associated with refractive index and its imaginary
part, i.e., extinction coefficient. The static value of the refractive
index n (0) is noted to be 1.5, which however remains unchanged with
increasing frequency till 5 eV. Nonetheless, its value grows gradually
beyond 5 eV and attains sharp peak at 7.5 eV frequency. Afterwards, the
sharp decrease in value of the refractive index has been noticed upto
12.5 eV, which re-escalates at further higher frequency. It has been
noticed that refractive index and extinction coefficient both have shown
similar pattern as that of the real and imaginary components of the
dielectric function. Likewise \(\varepsilon_{2}\), value of the
extinction coefficient remains zero equal to the energy band gap of the
considered compound, which is the characteristic of the semiconducting
materials [44].